Robust liveness enforcement of Petri nets with uncontrollable and unobservable transitions based on structural analysis

This paper concentrates on robust deadlock control problems for an automated manufacturing system with uncontrollable, unobservable events and resource failures, which is modeled by a subclass of Petri nets. A recovery subnet is added to the holder of each unreliable resource to model resource failure and recovery. In order to prevent a strict minimal siphon in a Petri net model from being emptied, an extended constraint set is constructed based on the complementary set of a strict minimal siphon to obtain a robust liveness constraint. Due to the uncontrollability and unobservability of the transitions, an automated manufacturing system cannot enforce inadmissible robust liveness constraints. It is necessary to decide the admissibility of robust liveness constraints and transform the inadmissible constraints into admissible ones. To this end, a monitor is designed for each admissible robust liveness constraint such that it can be enforced. Finally, an iterative algorithm is developed to perform the above steps and a robust liveness controlled system is obtained. The feasibility of the control strategy is demonstrated by examples.